Isaac Goldbring

activity

20232026

collaborators

7 papers

math.OA2026

Ultrapowers of spectral subspaces

Hiroshi Ando, Isaac Goldbring

We prove, for any W $^{*}$ -probability space $(M, φ)$ where $M$ is a type $III_{1}$ factor, any nontrivial, proper closed $F \subseteq R$ , and any nonprincipal ultrafilt…

math.OA2026

Model theory and Connes' bicentralizer problem

Hiroshi Ando, Isaac Goldbring

We make a series of model-theoretic contributions to Connes' bicentralizer problem, one of the most prominent open problems in the theory of von Neumann algebras. Our work builds o…

math.SP2025

A nonstandard approach to the direct integral version of the Spectral Theorem

Isaac Goldbring, Fabrice Nonez

We use nonstandard methods to prove the direct integral version of the Spectral Theorem for Unbounded Self-adjoint Operators. Our proof avoids the standard reduction to the case of…

math.LO2024

Effective subfactor theory

Alec Fox, Isaac Goldbring

We characterize when a subfactor $N \subseteq M$ is oracle computable relative to a presentation of the ambient factor $M$ in terms of computability of the Jones basic construction,…

math.LO2024

Back-and-forth equivalent group von Neumann algebras

Isaac Goldbring, Matthew Harrison-Trainor

We prove that if $G$ and $H$ are $α$ -back-and-forth equivalent groups (in the sense of computable structure theory) for some ordinal $α \geq ω$ , then their group von Neumann algebra…

math.LO2024

Computable Gelfand Duality

Peter Burton, Christopher J. Eagle, Alec Fox +5

We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to compu…

math.GR2023

A non-uniformly inner amenable group

Isaac Goldbring

We provide an example of two elementarily equivalent countable ICC groups $G$ and $H$ such that $G$ is amenable and $H$ is not inner amenable. As a result, we provide the first exa…